With recent progress in chirped pulse amplification (CPA) femtosecond laser systems, multi-PW peak powers and high focused intensities of 10^22-10^23 W/cm^2 have been made available. Because any laser pulses with intensities of 10^10-10^11W/cm^2 prior to the main femtosecond pulse are capable of ionizing solid targets and disturbing the laser plasma-interaction process, the temporal contrast has become one of the major issues in high-intensity laser-plasma experiments. Regarding the achievement of a high intensity contrast in the picosecond range after temporal compression, the main challenges are related to the decrease of amplified spontaneous emission, the improvement of the rising slope of the picosecond pedestal around the main pulse and the suppression of pre-pulses generated prior to the main pulse. Without special design constraints of PW-class CPA laser systems, post-pulses can be generated due to the laser pulses propagation through optical components. In many experiments the post-pulses can be ignored. However, due to the nonlinear response of any active medium, real pre-pulses can be generated by post-pulses, becoming one of the main issues in the experiments with tightly focused high power femtosecond laser pulses. The pre-pulses generation was one of the critical problems encountered in the early experiments with ELI-NP HPLS. Understanding the mechanism of pre-pulses generation by post-pulses and evaluating pre-pulses temporal characteristics are very important in the effort to reduce their intensity or even to suppress them. Considering the nonlinear modulation of the medium refractive index in the light field, which results by overlapping a main chirped laser pulse and its delayed replica, it was possible to calculate the pre-pulses contrast depending on the B-integral and the post-pulses contrast. Another approach for the investigation of pre-pulses generated by post-pulses is based on Kerr-effect induced four wave mixing (FWM) in the active medium and instantaneous frequency graphical representation of stretched laser pulses with large time-bandwidth product. This approach represents an intuitive way to understand the physical meaning of pre-pulses modifications: the frequency shift of pre-pulses compared to the main pulses, the temporal shape distortion after compression, the delay in relation to the mirrored position of the post-pulse versus the main pulse. Recent experimental investigations on the temporal contrast of pre-pulses generated by post-pulses were performed in a PW-class laser facility, J-KAREN-P, Kyoto, Japan. It was observed that the temporal and spectral characteristics of pre-pulses significantly differ from the main pulse and post-pulses, from which they were generated via “temporal diffraction”. These experimental results can be explained by considering the theoretical simulations based on FWM approach. Some technical solutions, implemented in this PW facility for suppressing pre-pulses by removing post-pulses, are discussed. Currently worldwide running home-made and commercial multi-PW CPA femtosecond lasers are still experimental systems. They must be improved step by step in accordance with the experimental needs.